Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story

Abstract

It has recently been shown that there exists a class of stable gapless spin liquids in 3+1 dimensions described by higher rank tensor U(1) gauge fields, giving rise to an emergent tensor electromagnetism. The tensor gauge field of these theories couples naturally to subdimensional particles (such as fractons), which are restricted by gauge invariance to move only along lower-dimensional subspaces of the system. We here work out some of the basic generalized electromagnetic properties of subdimensional particles coupled to tensor electromagnetism, such as generalized electrostatic fields, potential formulations, Lorentz forces, Maxwell equations, and Biot-Savart laws. Some concepts from conventional electromagnetism will carry over directly, while others require significant modification.

14+4 pages

References in corpus (10)

• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Glassy quantum dynamics in translation invariant fracton models
• Fracton topological order via coupled layers
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• Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
• Novel Algebraic Boson Liquid phase with soft Graviton excitations
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• An apparent paradox concerning the field of an ideal dipole

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